Known fasteners of this kind include a base element sandwiching the carpet and a female element sandwiching the mat. The base element includes a head that projects from the carpet and the female element is adapted to cooperate with the head of the base element to fix the mat to the carpet.
DE 196 17 408 describes such fasteners. The head of the base element is mushroom-shaped and includes a shoulder. The female element has a series of teeth one end of which is attached to the rest of the female element and the free end of which is hook-shaped. The teeth have a height that enables them to flex. When the female element is moved toward the base element, and thus when the teeth are moved toward the head, the free ends are pushed back and then locate on the shoulder.